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From Page 4, last paragraph of David Burch's article: "...or use the purely fictitious sight at 47:02 with an Hs of 27° 19.0'. We did not actually measure a height at this last time, but if we had, that is most likely what we would have gotten."

I have tried this a couple of times, when none of my actual sights were quite right, extrapolating from the slope both a fictitious time and a fictitious sextant altitude, and gotten an LOP within less than 2 nm of my position.

Somehow, when you are doing this, "sight averaging" doesn't seem to be quite the right name for what you are doing, but I could think of no other descriptive term to use in its place.